3.4. Comparison and interpretation
Many galaxies contain a substantially larger number of luminous X-ray sources in globular clusters than our own galaxy (compare Tables 1, 3). This can be explained by their larger numbers of globular clusters. The fraction of globular clusters that contains a luminous X-ray source is roughly constant between galaxies, as is the number of X-ray sources in clusters scaled on cluster luminosity or mass (2 × 10-7 L , I-1 for Lx > 3 × 1037erg s-1, Sarazin et al. 2003, Kundu et al. 2003). Similarly, the larger number of globular cluster X-ray sources in M31 compared to the Milky Way may be explained by the larger number of clusters (Supper et al. 1997, Di Stefano et al. 2003). In several elliptical galaxies, the X-ray luminosity functions of the luminous LMXBs located in globular clusters show a knee near the Eddington luminosity for an accreting neutron star. In analogy with the luminosity distribution in the Milky Way (Grimm et al. 2002), this suggests that many of the sources with luminosities above the knee may be accreting black holes. This suggestion is supported in some cases by the X-ray spectrum, which shows the soft signature of an accreting black hole (e.g. Angelini et al. 2001). It is noted by Kim & Fabbiano (2003b) that selection effects should be taken into account in deciding whether a break is real. The fact that a very luminous accreting black hole is not found in the globular clusters of the Milky Way is probably due to the small number of cluster sources.
The X-ray sources are found preferably in optically bright clusters (Angelini et al. 2001). This could be explained as a scaling with mass (Kundu et al. 2002, Sarazin et al. 2003). We suggest, however, that the scaling with mass is a proxy for the scaling with the collision number, caused by the strong correlation between mass and collision number. In the Milky Way, the probability of a cluster to contain a luminous X-ray source scales better with the collision number than with the mass (Verbunt & Hut 1987; Pooley et al. 2003).
In many galaxies, luminous X-ray sources are found preferably in red, metal-rich clusters. Bellazzini et al. (1995) demonstrated this for the Milky Way (see Figure 7) and less conclusively for M31. Di Stefano et al. (2003) find in their sample of M31 clusters that the probability that a cluster contains an X-ray source is not strongly correlated with metallicity. Kundu et al. (2002) find that a red cluster in NGC4472 has a 3 times higher probability of hosting a luminous X-ray source than a blue cluster. A similar result is found for NGC4365 by Sarazin et al. (2003), and for NGC3115 by Kundu et al. (2003). We consider four suggested explanations. First, if metal-rich clusters are younger, they contain main-sequence stars of higher mass, which are thought to be more efficient in forming an X-ray binary (Davies & Hansen 1998). In NGC4365 such a young population is indeeed present, but it does not show an increased formation rate of X-ray sources (Kundu et al. 2003). Also, the preference for metal-rich clusters is observed in the Milky Way and in NGC3115, where all globular clusters are old. These results show that metallicity, not age, must explain the preference of X-ray sources for red clusters (Kundu et al. 2003). Second, a higher X-ray luminosity at higher metallicity would produce a preference for metal-rich clusters in a flux-limited sample. Various models have been suggested to produce higher X-ray luminosities in binaries with a donor of higher metallicity (e.g. Bellazzini et al. 1995, Maccarone et al. 2003b). However, X-ray sources in metal-rich clusters are not observed to be more luminous than those in metal-poor clusters in M31 (Verbunt et al. 1984) or, with less statistical constraint, in NGC4472 (Maccarone et al. 2003a). Third, Grindlay (1987) suggests that metal-rich clusters have a flatter initial mass function (and hence more neutron stars). However, such a dependence is not observed in the Milky Way (Piotto & Zoccali 1999). Finally, Bellazzini et al. (1995) suggest that the longer life times and larger radii of metal-rich stars enhance their capture rate; the capture probability is proportional to radius (see Eq. 5 below), and it must be doubted that the small difference in radii has sufficient effect to explain the observations. It is fair to say that the connection between metallicity and the occurrence of LMXBs in globular clusters is not yet well understood.
Figure 7. Left: central density of globular clusters in the Milky Way as a function of metallicity. Filled circles indicate globular clusters with a luminous X-ray source. Even at the same density there is a preference for high-metallicity clusters. After Bellazzini et al. (1995). Right: the preference for high-metallicity clusters persists in a plot of collision number as a function of metallicity.
There is a tendency for X-ray sources in metal-rich globular clusters to have softer X-ray spectra (M31: Irwin & Bregman 1999, NGC4472: Maccarone et al. 2003a).